On the Number of Bits to Encode the Outputs of Densely Deployed Sensors
Suppose M sensors are densely deployed throughout some bounded geographical region in order to sample a stationary two-dimensional random field, such as temperature. Suppose also that each sensor encodes its measurements into bits in a lossy fashion for transmission to some collector or fusion center where the continuous-space field is reconstructed. We consider the following question. If the distortion in the reconstruction is required to be D or less, what happens to the total number of bits produced by the encoders as the sensors become more numerous and dense? Does the increasing number of sensors mean that the total number of bits increases without limit? Or does the increasing correlation between neighboring sensor values sufficiently mitigate the increasing number of sensors to permit the total number of bits to remain bounded as M increases?
KeywordsMean Square Error Distortion Function Scalar Quantization Test Channel Gaussian Source
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